Overall a draw was about right in an evenly contested game which saw Peterhead create the best chance of the first in the 24th minute.
Keith Gibson headed the ball down for Martin Wood, who volleyed narrowly wide of the left hand post.
Brechin also had their chances and home keeper Paul Mathers had to save from Stuart Callaghan and Scott Walker.
The second half was only three minutes old when Peterhead went in front. Wood sent Martin Bavidge clear and he squared the ball from the left side of the box for Gibson to score at the back post from a tight angle.
Graeme Sharp could have wrapped up the game three minutes later but City keeper Craig Nelson made the first of several fine saves to deny him.
Brechin levelled in the 58th minute. A corner from the left broke to a trialist who had come on as a sub and his shot from just inside the area went into the net through a ruck of players.